Math / Data & Statistics

QuestionC https://learn.hawkeslearning.com/Portay/L inport favorites B. Booking.com McAfee Security There are 37 students in the University Travel Club. The following information and Venn diagram show how many students traveled to Germany, France, and Spain. How many students have been to France or Spain but not Germany? 17 members have visited Germany 13 have been to Spain 19 have visited France 10 have been to Germany and France 6 have only been to France 5 have only been to Germany 3 have been to only Spain and France 3 have been to all three countries Some of the members have not been to any of the three Tutor Send to Instructor Skip Try Similar Submit $A$

Studdy Solution

STEP 1

1. We are given the total number of students and the number of students who visited each country and some combinations of countries.
2. We need to find the number of students who have been to France or Spain but not Germany.

STEP 2

1. Define the variables for each subset of the Venn diagram.
2. Use the given information to set up equations for the subsets.
3. Calculate the required subset using the equations.

STEP 3

Define the variables for the subsets of the Venn diagram: - $G$ : Number of students who visited Germany. - $F$ : Number of students who visited France. - $S$ : Number of students who visited Spain. - $GF$ : Number of students who visited both Germany and France. - $GS$ : Number of students who visited both Germany and Spain. - $FS$ : Number of students who visited both France and Spain. - $GFS$ : Number of students who visited Germany, France, and Spain. - $G' \cap F \cap S$ : Number of students who visited France or Spain but not Germany.

STEP 4

Use the given information to set up equations:
1. $G = 17$
2. $S = 13$
3. $F = 19$
4. $GF = 10$
5. $FS = 3$ (only Spain and France)
6. $GFS = 3$
7. $G \setminus (F \cup S) = 5$ (only Germany)
8. $F \setminus (G \cup S) = 6$ (only France)

STEP 5

Set up an equation for students who visited only Spain: $S \setminus (G \cup F) = S - (GS + FS + GFS) = 13 - (GS + 3 + 3) = 13 - GS - 6$ Since there's no information about students who visited only Germany and Spain, we assume $GS = 0$ .

STEP 6

Calculate the number of students who visited only Spain: $S \setminus (G \cup F) = 13 - 6 = 7$

STEP 7

Calculate the number of students who visited France or Spain but not Germany: $(F \setminus (G \cup S)) + (S \setminus (G \cup F)) + (FS) = 6 + 7 + 3 = 16$
Solution: The number of students who have been to France or Spain but not Germany is $16$ .

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Studdy Solution

STEP 1

1. We are given the total number of students and the number of students who visited each country and some combinations of countries.
2. We need to find the number of students who have been to France or Spain but not Germany.

STEP 2

1. Define the variables for each subset of the Venn diagram.
2. Use the given information to set up equations for the subsets.
3. Calculate the required subset using the equations.

STEP 3

STEP 4

Use the given information to set up equations:
1. $G = 17$
2. $S = 13$
3. $F = 19$
4. $GF = 10$
5. $FS = 3$ (only Spain and France)
6. $GFS = 3$
7. $G \setminus (F \cup S) = 5$ (only Germany)
8. $F \setminus (G \cup S) = 6$ (only France)

STEP 5

Set up an equation for students who visited only Spain: $S \setminus (G \cup F) = S - (GS + FS + GFS) = 13 - (GS + 3 + 3) = 13 - GS - 6$ Since there's no information about students who visited only Germany and Spain, we assume $GS = 0$ .

STEP 6

Calculate the number of students who visited only Spain: $S \setminus (G \cup F) = 13 - 6 = 7$

STEP 7

Calculate the number of students who visited France or Spain but not Germany: $(F \setminus (G \cup S)) + (S \setminus (G \cup F)) + (FS) = 6 + 7 + 3 = 16$
Solution: The number of students who have been to France or Spain but not Germany is $16$ .

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Studdy Solution

STEP 1

1. We are given the total number of students and the number of students who visited each country and some combinations of countries.2. We need to find the number of students who have been to France or Spain but not Germany.

STEP 2

1. Define the variables for each subset of the Venn diagram.2. Use the given information to set up equations for the subsets.3. Calculate the required subset using the equations.

STEP 3

STEP 4

STEP 5

STEP 6

Calculate the number of students who visited only Spain: S∖(G∪F)=13−6=7 S \setminus (G \cup F) = 13 - 6 = 7 S∖(G∪F)=13−6=7

STEP 7

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. We are given the total number of students and the number of students who visited each country and some combinations of countries.
2. We need to find the number of students who have been to France or Spain but not Germany.

1. Define the variables for each subset of the Venn diagram.
2. Use the given information to set up equations for the subsets.
3. Calculate the required subset using the equations.

Calculate the number of students who visited only Spain: $S \setminus (G \cup F) = 13 - 6 = 7$